Chapter 1 Flashcards
What is the Schrodinger equation?
iℏ(∂𝚿/∂t) = −(ℏ^2/2)(∂^2𝚿/∂x^2) + V𝚿
What does the Schrodinger equation determine?
The Schrodinger equation determines 𝚿(x,t) for all future time
What is a wave function, what does it do, and how does it represent the state of a particle, according to Born’s statistical interpretation?
|𝚿(x,t)|^2 gives the probability of finding a particle at point x at time t, when integrated by dx from points a to b
What is indeterminacy in the context of quantum mechanics?
Even if you know everything the theory has to tell you about a particle, still you cannot predict with certainty the outcome of a simple experiment to measure its position–all quantum mechanics has to offer is statistical information about the possible results
What is the orthodox school of thought regarding quantum indeterminacy?
The particle wasn’t really anywhere. It was the
act of measurement that forced it to “take a stand” (though how and why it decided on the point C we dare not ask). Jordan said it most starkly: “Observations not only disturb what is to be measured, they produce it . . .We
compel [the particle] to assume a definite position.” This view (the so-called
Copenhagen interpretation), is associated with Bohr and his followers. Among physicists it has always been the most widely accepted position. Note, however, that if it is correct there is something very peculiar about the act of measurement—something that almost a century of debate has done precious
little to illuminate.
If a particle was measured to be at a point C, what would result from measuring the position of that particle immediately after the first measurement?
The repeated measurement would return the same value. The first measurement radically alters the wave function to the point where it collapses to spike at point C, but it quickly spreads out again after measurement.
What is the expectation value in quantum mechanics?
The expectation value is the probabilistic expected value of the result (measurement) of an experiment. It can be thought of as an average of all the possible outcomes of a measurement as weighted by their likelihood, and as such it is not the most probable value of a measurement; indeed the expectation value may have zero probability of occurring.
How do we preserve the normalization of the wave function with the Schrodinger equation?
The Schrodinger equation preserves the normalization automatically
According to the de Broglie formula, what two factors correspond to one another in a quantum mechanical wave function?
Wavelength and momentum
What is Heisenberg’s uncertainty principle?
The standard deviation of position x times the standard deviation of momentum p is greater than or equal to ℏ/2. Like position measurements, momentum measurements yield precise answers—the “spread” here refers to the fact that measurements made on identically prepared systems do not yield identical results.